对月球形状的估算

The Estimate on Lunar Figure

1799年，Laplace发现月球的3个主惯量矩，与月球的轨道和自转状态并不相符．有些学者认为，这可能是现在的月球仍保留了早期的“化石”形状．大约在三十多亿年前，月球曾经离地球很近并且转得较快，然后月球逐渐迁移远离地球并且转动得慢了下来．在此迁移的较早时期，月球受到了引潮力和自转离心力的作用，成为一个椭球体．并且很快凝固．所幸的是，固态月球的岩石圈较为稳定，使我们现在仍然能够看到很早时期月球的形状．文中利用月球天平动参数以及引力场系数，计算了椭球体3个主向径a，b，c的长度和月球的平衡潮形状，得到如下3个结论：（1）开始时月球离地球是非常近的，大约在三十亿年前月球可能已经冷却和固化，现在的月球基本上保留了凝结时的形状．（2）证明了液态月球的潮汐形变是月球平衡潮高度的1．934倍．因此用月球引力场推算月球形状时，必需考虑到流体勒夫数hf=1．934的影响．（3）根据月球三个主轴a，b，c的长度之差，推算了月球临凝固时的月地距离为1．7455×10^8m，自转周期为3．652day．从而推算出月球临凝固时的恒星月长度为8．34day．因此在月球凝结时，月球被锁定在与自转速率比为2：1的共振轨道上．

In 1799 Laplace had discovered that the lunar three principal momentum are not in equilibrium with the Moon＇s current orbital and rotational state.Some authors suggested that the Moon may carry a fossil figure. Before more 3 billion years the liquid Moon was closer to the Earth and revolved faster.Then the Moon migrated outwards and revolved slow down. During the early part of this migration, the Moon was continually subjected to tidal and rotational stretching and formed into an ellipsoid. Then the Moon cooled and solidified quickly. Eventually, the solid Moon＇s lithosphere was stable, so that we may see the very early lunar figure. In this paper, by using the lunar libration parameters and the spherical-harmonic gravity coefficient, the length of three radii a, b, c of the ellipsoid and the Moon＇s figure as an equilibrium tidal have been calculated. Then three conclusions can be obtained; （1） In the beginning the Moon may be very close to the Earth, before about 3 billion years the moon may cooled and solidified, and the present Moon are in the fossil figure. （2） In the third section of this paper, we demonstrate that the tidal deformation of liquid Moon was 1.934 times then the equilibrium tide. So that if to calculating the true lunar figure by using the lunar spherical-harmonic gravity coefficients, the effects of Liquid Love number hf= 1.934 must be considered. （3） According to the difference between a, b and c, the lunar distance （1.7455 × 10^8 m） and spin period 3.652day can be calculated. So that the lunar orbits period was 8.34day. Hence the Moon was locked closely into a resonance orbit in the ratio 2 ： 1 when the Moon froze.